Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result
Title | Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result PDF eBook |
Author | Valentin Poenaru |
Publisher | American Mathematical Soc. |
Pages | 104 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821834606 |
Shows that at the cost of replacing $V DEGREES3$ by $V_h DEGREES3 = \{V DEGREES3$ with very many holes $\}$, we can always find representations $X DEGREES2 \stackrel {f} {\rightarrow} V DEGREES3$ with $X DEGREES2$ locally finite and almost-arborescent, with $\Psi (f)=\Phi (f)$, and with the ope
Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
Title | Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness PDF eBook |
Author | Lee Klingler |
Publisher | American Mathematical Soc. |
Pages | 187 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821837389 |
This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)
Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity
Title | Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity PDF eBook |
Author | Mike Field |
Publisher | American Mathematical Soc. |
Pages | 113 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821835998 |
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).
The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
Title | The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups PDF eBook |
Author | Martin W. Liebeck |
Publisher | American Mathematical Soc. |
Pages | 242 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821834827 |
Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
Maximum Principles on Riemannian Manifolds and Applications
Title | Maximum Principles on Riemannian Manifolds and Applications PDF eBook |
Author | Stefano Pigola |
Publisher | American Mathematical Soc. |
Pages | 118 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821836390 |
Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring
Title | A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring PDF eBook |
Author | Ehud Friedgut |
Publisher | American Mathematical Soc. |
Pages | 80 |
Release | 2006 |
Genre | Mathematics |
ISBN | 0821838253 |
Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper the authors establish a sharp threshold for random graphs with this property. Let $G(n, p)$ be the random graph on $n$ vertices with edge probability $p$. The authors prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n, (1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[ G(n, (1]\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1.$. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setti
Kahler Spaces, Nilpotent Orbits, and Singular Reduction
Title | Kahler Spaces, Nilpotent Orbits, and Singular Reduction PDF eBook |
Author | Johannes Huebschmann |
Publisher | American Mathematical Soc. |
Pages | 110 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821835726 |
For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.